Gross and Yang [1]}, first found an example of a \( URSE \)  which is \( \mathcal {S}=\lbrace z: e^z+z=0\rbrace  \) , and as this an infinite set, so it is very natural to investigate whether there exists a finite \( URSE \)  or not. In \( 1995,\)  Yi [2]} who found a \( URSE \)  \( \mathcal {S}=\lbrace z: z^n+az^m+b=0\rbrace  \) , where \( n>2m+4 \)  and \( a,\; b \)  chosen in a such a way that the equations \( z^n+az^m+b=0 \)  has no repeated roots. Since then there have been many efforts to study the problem of constructing \( URSE \)  time to time (see [3]}, [4]}, [5]}). There is another study on the \( URSE \)  of entire functions, which is to seek a set \( \mathcal {S} \)  for which if \( E_f(\mathcal {S})=E_{f^{\prime }}(\mathcal {S}) \) , then \( f\equiv f^{\prime } \) . One can verify that the form of the function will be \( f(z)=ce^{z}. \)  where \( c \)  is a non-zero complex number. Li and Yang [6]} also deduced that if \( E_f(\mathcal {S})=E_{f^{\prime }}(\mathcal {S}) \) , where \( \mathcal {S}=\lbrace a,b\rbrace  \)  with \( a+b\ne 0 \) , then either \( f(z)=\mathcal {A}e^z \)  or \( f(z)=\mathcal {A}e^z+a+b \) , where \( \mathcal {A} \)  is a non-zero complex number. Later, Fang and Zalcman [7]}, using the theory of normal families, proved that there exists a set \( \mathcal {S}=\lbrace a, b, c\rbrace  \)  such that \( E_f(\mathcal {S})=E_{f^{\prime }}(\mathcal {S}) \) , then \( f\equiv f^{\prime }. \)  A special topic widely studied in the uniqueness theory is the case when \( f(z) \)  shares value(s) or set(s) with its derivatives or differential polynomials. We recall a result of this type from the preceding literature:
